To a standing ovation from the public gallery, the ACT government introduced its marriage equality bill on Thursday. It is set to pass the territory assembly, giving gay and lesbian couples from the ACT and interstate the right to marry in Canberra by the end of the year.

The Australian Christian Lobby has called on the federal parliament to override the territory law and has consulted lawyers about a possible legal challenge against the new laws.

Abbott said the new attorney-general, George Brandis, was seeking legal advice.

"The ACT is entitled to do what it can within the law," he said. "As you know, under the constitution the Commonwealth has responsibility for marriage and the attorney-general will be seeking advice on precisely how far the ACT can go on this."

The Commonwealth’s power to disallow laws made in the territory was weakened in the last parliament and now requires legislation to be passed through both the House of Representatives and the Senate, making it much more difficult than when the Howard government overturned an attempt by the ACT to legalise same sex marriage seven years ago.

It is also possible for the ACT law to be challenged in the high court as being incompatible with the federal Marriage Act, which the Howard government amended to define marriage as the union of a man and a woman.

Leading constitutional lawyer George Williams believes that under the constitution the federal parliament has "a concurrent, rather than exclusive power” to make laws on marriage, but others believe a challenge could be successful.

The ACT chief minister, Katy Gallagher, said the ACT had legal advice that shows that a bill “that did not contradict the federal Marriage Act would be constitutionally valid”. Gallagher said the ACT law could work “alongside the Commonwealth Marriage Act”.

"It comes with risks about potential challenges to the legislation but, again, we don't believe that should stop us pursuing a commitment we have made,” she said, describing the introduction of the bill as “a proud moment for all of us”.

Lyle Shelton, managing director of the Australian Christian Lobby, told Guardian Australia he was seeking legal advice about a possible challenge, but believed it would be better for the law to be overturned by the federal parliament.